I agree with Cameron. I don't know your SUV but it sounds like one or more of your engine mounts has failed,
I would assume that you SUV is a rear wheel drive. There are a few things to try:
Try Balancing your Tyres
Check Prop Shaft and Universal Joints and mostly the centre carrier bearing.
Check you engine mountings
Hope this helps
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When I accelerate the SUV the whole van starts trembling/shaking if I pull off the gas...it shakes less. No problem with tires.
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